x/9x-72=6x+48

Solution for x/9x-72=6x+48 equation:

x/9x-72=6x+48

We move all terms to the left:

x/9x-72-(6x+48)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We get rid of parentheses

x/9x-6x-48-72=0

We multiply all the terms by the denominator


x-6x*9x-48*9x-72*9x=0

Wy multiply elements

-54x^2+x-432x-648x=0

We add all the numbers together, and all the variables

-54x^2-1079x=0

a = -54; b = -1079; c = 0;
Δ = b2-4ac
Δ = -10792-4·(-54)·0
Δ = 1164241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1164241}=1079$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1079)-1079}{2*-54}=\frac{0}{-108}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1079)+1079}{2*-54}=\frac{2158}{-108}
=-19+53/54
$